BibTex RIS Kaynak Göster

HİZMET SÜRESİ HİPO-ÜSTEL DAĞILIMA UYAN KUYRUK MODELİNDE, NEUTS’UN MATRİS-GEOMETRİK YÖNTEMİNİN SİMULASYON YARDIMI İLE ERGODİKLİK SONUÇLARI VE PERFORMANS ÖLÇÜLERİNİN ELDE EDİLMESİ

Yıl 2018, Cilt: 3 Sayı: 2, 61 - 77, 01.11.2018

Öz

Bu çalışmada, varış süresi parametreli üstel dağılım ve hizmet içi HipoÜstel dağılım içeren bir kuyruk modeli incelendi. Müşteri sisteme geldiğinde, kuyrukta veya hizmet kanalında müşteri varsa, hizmet almak için kuyrukta beklemeye başlar ve müşterinin kaybolmasına izin verilmez. FIFO yönteminin kuyruk disiplini olarak kullanıldığı bu modelde, diyagram sistemde müşteri sayısını ve hizmet alan istemcinin hangi aşaması olduğunu gösteren geçiş hızı diyagramını gösterir. Buna göre, tridiagonal matris ve matris alt matrisleri inşa edilmiştir. ve matrisleri bu alt matrislerin yardımı ile hesaplanır. Neuts’un matrisi, bu matrislerin bir fonksiyonu olan sırası uygulanan yineleme tarafından elde edilir. Homojen doğrusal denklemler sisteminin çözümü için kararlı durumlu alt kümeler olan bu R matrisi olasılık vektörü , olarak hesaplanır. başlangıç değerine ve ’a bağlı olarak elde edilir. Sistem parametrelerinin gerçek olasılıkları, çözüm ve sayısal analizlerin normalleştirilmesi ile hesaplanır.

Kaynakça

  • Artalejo, J. R. & Choudhury, G. (2004). Steady-State analysis of an M/G/1 queue with repeated attempts and two-phase service. Quality Technology & Quantative Management, Vol.1, No.2, pp. 189
  • De Muynck, M., Bruneel, H. & Wittevrongel, S. (2017). Anaysis of a discrete-time queue with general service demands and phase-type service capacities, Journal of Industrial and Management
  • Optimisation, 2017, Doi: 10.3934/jimo.20170204, Volume: 13, Issue: 4, Pages: 1901-1926.
  • Jackson, R. R. P. (1954). Queueing systems with Phase-Typeservice. Operat. Res. Quart., 5, 109-120.
  • Neuts, M. F. (1981). Matrix-Geometric solutions in stochastic models, an algoritthmic approach, John
  • Hopkins University Press, Baltimore. Ramaswami, V. & Neuts, M. F. (1980). A duality theorem for phase type queues. The Annals of Probability, Vol.8, No.5, 974-985.
  • Rana, R. K. (1972). Queueing problems with arrivals in general stream and phase type service. Metrika, vol. 18, no. 1, pp. 69–80.
  • Sağlam, V. & Zobu, M. (2013). Control of Traffic Intensity in Hyperexponential and Mixed Erlang
  • Queueing System with a Method Based on SPRT, MATHEMATICHAL PROBLEMS IN ENGINEERING, 2013, 241241, 6 / 2013, 10.1155.
  • Sağlam V., Zobu, M., Yücesoy, E. & Sağır, M. (2016). The simulation and control of traffic intensity in Hypoexponential and Coxian queueing systems with a method based on sequential probability ratio tests, International Journal of Sciences: Basic and Applied Research, No.4, 122-137.
  • Smaili, K., Kadri, T. & Kadry, S. (2013). Hypoexponential distribution with different parameters, Applied Mathematics, 624-631.
  • Stewart, W. J. (2009). Probability, Markov Chains, Queues and Simulation, Princeton University Press, United Kingdom.

On Obtaining Of Ergodicity Results And Performance Measures Of Hypo-Exponential Distributed Queuing Model With Neuts Matrix-Geometric Method

Yıl 2018, Cilt: 3 Sayı: 2, 61 - 77, 01.11.2018

Öz

In this study, a queuing model with exponential distribution and inter-service hypo-exponential distribution with inter-arrival time parameter was studied. When the customer arrives in the system, if there are customers in the queue or service channels, they start to wait in the queue to get service, and the customer is not allowed to lose. In this model where FIFO method is used as queue discipline, the diagram shows the number of customers in the system and the transition rate diagram for the showing which phase the client receiving the service is. Accordingly, the tridiagonal matrix and the sub-matrices of the matrix are constructed. The matrices and are calculated with the help of these submatrices. Neuts' matrix is obtained by the iteration applied on the sequence which is defined as a function of these matrices. The probability vector from this matrix , which is the steady-state subvectors for the solution of the system of homogeneous linear equations, is computed as , are obtained based on the initial value and depending on . The actual probabilities of the system parameters are calculated by normalizing the solution and numerical analysis.

Kaynakça

  • Artalejo, J. R. & Choudhury, G. (2004). Steady-State analysis of an M/G/1 queue with repeated attempts and two-phase service. Quality Technology & Quantative Management, Vol.1, No.2, pp. 189
  • De Muynck, M., Bruneel, H. & Wittevrongel, S. (2017). Anaysis of a discrete-time queue with general service demands and phase-type service capacities, Journal of Industrial and Management
  • Optimisation, 2017, Doi: 10.3934/jimo.20170204, Volume: 13, Issue: 4, Pages: 1901-1926.
  • Jackson, R. R. P. (1954). Queueing systems with Phase-Typeservice. Operat. Res. Quart., 5, 109-120.
  • Neuts, M. F. (1981). Matrix-Geometric solutions in stochastic models, an algoritthmic approach, John
  • Hopkins University Press, Baltimore. Ramaswami, V. & Neuts, M. F. (1980). A duality theorem for phase type queues. The Annals of Probability, Vol.8, No.5, 974-985.
  • Rana, R. K. (1972). Queueing problems with arrivals in general stream and phase type service. Metrika, vol. 18, no. 1, pp. 69–80.
  • Sağlam, V. & Zobu, M. (2013). Control of Traffic Intensity in Hyperexponential and Mixed Erlang
  • Queueing System with a Method Based on SPRT, MATHEMATICHAL PROBLEMS IN ENGINEERING, 2013, 241241, 6 / 2013, 10.1155.
  • Sağlam V., Zobu, M., Yücesoy, E. & Sağır, M. (2016). The simulation and control of traffic intensity in Hypoexponential and Coxian queueing systems with a method based on sequential probability ratio tests, International Journal of Sciences: Basic and Applied Research, No.4, 122-137.
  • Smaili, K., Kadri, T. & Kadry, S. (2013). Hypoexponential distribution with different parameters, Applied Mathematics, 624-631.
  • Stewart, W. J. (2009). Probability, Markov Chains, Queues and Simulation, Princeton University Press, United Kingdom.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Bölüm Research Article
Yazarlar

Murat Sağır

Yayımlanma Tarihi 1 Kasım 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 3 Sayı: 2

Kaynak Göster

APA Sağır, M. (2018). HİZMET SÜRESİ HİPO-ÜSTEL DAĞILIMA UYAN KUYRUK MODELİNDE, NEUTS’UN MATRİS-GEOMETRİK YÖNTEMİNİN SİMULASYON YARDIMI İLE ERGODİKLİK SONUÇLARI VE PERFORMANS ÖLÇÜLERİNİN ELDE EDİLMESİ. Uluslararası Medeniyet Çalışmaları Dergisi, 3(2), 61-77. https://doi.org/10.26899/inciss.173